The US v. North Korea: The role of game theory

Tension between the United States and North Korea has reached a stage where missile strikes have become an alarming possibility. If tensions escalate further to a state where military action looks almost certain, game theory could offer us insight into finding the best strategy to tackle the problem.

Firstly though, what does Kim Jong Un hope to achieve by possessing a nuclear arsenal? It is most likely that he sees nuclear weapons as a guarantee of his regime. Possession of a nuclear arsenal would likely prevent interference from the West due to the threat it would pose. Having seen what happened to Colonel Gaddafi after nuclear disarmament and NATO intervention in Libya, Kim Jong Un may see a nuclear arsenal as a necessity.

So, what about game theory? Game theory has a role in deterrence strategy – whether it be nuclear deterrence or simply the deterrence of new firms from entering a market by existing ones. Herman Kahn, a US nuclear strategist during the Cold War and the inspiration for Stanley Kubrick’s character Dr. Strangelove, created an early game-theoretic model of nuclear deterrence after taking inspiration from a game known as “Chicken”: two cars drive quickly towards each other and the one to steer out of the path of the other loses. The model for the game is simple in that the drivers, let’s call them Kim and Donald, can either “stick” or “swerve” and the order of preference is as follows: win (1st), draw (2nd), lose (3rd), death (4th). In this game, there are two Nash equilibria, where either Kim or Donald wins:

Stick

Swerve

Stick

Death

Death

Lose

Win

Swerve

Win

Lose

Draw

Draw

However, this model is admittedly too extreme a simplification to be applied to actual nuclear strategy. A country does not devise an optimal strategy from the start of the crisis, as implied by Kahn’s model, but it acts in response to the decisions of its enemy as the crisis escalates and can reconsider its decisions if circumstances change.

What this model does illustrate is brinkmanship: the idea that a player pursues a dangerous policy or strategy to the brink of disaster, causing the opponent to surrender. Brinkmanship was notoriously used during the Cuban Missile Crisis, but the outcome was not as favorable to the Soviet Union, who incited it.

It is also worth looking more closely at the order of preference in the model. In the game of Chicken, the cost of death is seen to greatly exceed the cost of losing. However, in a nuclear crisis, things may be different: for a country, the cost of an enemy takeover may exceed the cost of death from a nuclear warhead. This may even be the case when there is a scenario of total annihilation, as long as the destruction is mutually assured. So, if the order of preference is changed, the model should also be changed (this time, let’s change it to “nuke” and “back down” instead of saying “stick” and “swerve,” and let’s also use payoff values instead of “win,” “lose,” “draw,” and “death”):

Nuke

Back Down

Nuke

-2

-2

-3

2

Back Down

2

-3

1

1

Now, you may notice that this particular payoff matrix bears resemblance to the Prisoner’s Dilemma, where the dominant strategy is to betray the other player. The equivalent strategy in this particular model is to nuke the other player. So, if the dominant strategy is a nuclear strike, why did the Cold War stay cold?

The answer to this question boils down to the fact that, as is the case in the game of Chicken, this is much too simple a model to properly illustrate nuclear strategy: this model does not demonstrate the step-by-step process of decision-making that takes place as tensions escalate.

Then how do nuclear strategists devise a dominant strategy? Well, by combining these two models and developing them to factor in the step-by-step process of decision-making and retaliation, a dominant strategy can be arrived at. However, it is important to realise that there is no explicit dominant strategy as it depends on what has been factored in and excluded in the creation of the model.

An example of a Nash equilibrium of one of these more developed game-theoretic models was the doctrine of mutually assured destruction (MAD), where the use of nuclear weapons by either an attacker or a defender leads to the total annihilation of both sides. The prospect of total annihilation prevents one side from launching a preemptive nuclear strike, stopping the other from using their own nuclear weapons leading to a stalemate. This doctrine was adopted in the Cold War, which is why the nuclear stalemate existed.

However, nuclear deterrence compares the credibility of a threat to the rationality behind it. If a threat is not credible, it is unlikely to have an effect on the course of action of the opponent. In terms of nuclear deterrence, something that can boost the credibility of the threat of a nuclear strike is the previous use of a nuclear weapon. America has used nuclear weapons at Hiroshima and Nagasaki, making their threat very credible whereas North Korea possesses no such history.

Nevertheless, Kim Jong Un has created a brutal regime; his brutality, and the fact that he has disregarded nuclear sanctions and regulations, increases the credibility of his threat. But, if credibility can be influenced by the character of the decision-making authority, then Donald Trump’s ruthless, business-like approach should certainly boost the US’ credibility too.

If nuclear deterrence strategy is to work so that nuclear warfare can be prevented, both the attacker and the defender have to be rational decision-makers. Nobody can be certain whether Kim Jong Un is rational or not, but we should desperately hope that he is.